Phase transitions in multiband periodic all-dielectric photonic structures

We study multiband metamaterials with several spectral band gaps associated with local Mie resonances, for the example of a square lattice of dielectric rods with dielectric permittivity ϵ = 70. We find that the band diagram possesses three Mieresonance gaps, all corresponding to negative effective magnetic permeability. By analysing the wave-propagation patterns, we demonstrate that this periodic structure can be homogenized only in the frequency range below the lowest Bragg-gap frequency. We study the predicted effects experimentally by measuring the transmission spectra at the microwaves and find an excellent agreement with theoretical results.